complete state of affairs and an infinite set of events in one go. Imagine the following scenarios:

-1- -2- EPISTEMOLOGY AND METHODOLOGY 3. We are in a physics laboratory and make the observation that all objects fall at a uniform Can we solve the problem of induction, and if not, to what extent is it really a problem? (2493 words 1 ) acceleration in a vacuum. Maybe with the help of some theory we conclude that all objects - regardless of shape, size or mass - fall at a uniform acceleration in a vacuum. We also conclude that this will always be the case in the future. In this case we have again reached a general conlusion. But in this case we have reached a conclusion about a 1. Introduction complete state of affairs and an infinite set of events in one go. Imagine the following scenarios: In all three of the above examples we have reached a general conclusion from a finite or incomplete number of observations. This is what's known as induction or inductive 1. We are out on a boating cruise in the Pacific Ocean and discover a new island. Upon entering the island we are greeted by a flock of blue birds with very distinguishing features (they can't fly because their wings are upside-down, causing them to flap into the ground whenever they want to take off). For the first few days, we are scouting the island inference. In the first example our inductive inference was about things as they are everywhere. In the second example it was about things as they are forever. And in the third example - typically for science - the induction tells us what things are like everywhere and forever. and constantly come across these blue birds with upside-down wings. There are many other birds around on the island, but all of them can fly. All the birds we have encountered so far with upside-down wings are blue. After a while we conclude that all the birds on the island with upside-down wings are blue. We have reached a general conclusion about a complete set of states of affairs from observation of an incomplete set of states of affairs. 2 Induction is opposed to deduction, where a true general conclusion is reached from premises in virtue of the fact that the truth of the premises does not allow for the falsehood of the conclusion. This, however, is not the fact with induction: the truth of an inductively reached conclusion can not be guranteed by the truth of its premises. And this is exactly where a big problem arises, namely the problem of induction. 2. Every day we get up in the morning and our room is filled with sunlight. This does not in any way surprise us: the sun has risen every day of our lives and we assume that it will continue doing so for ever. Again, we have reached a general conclusion. This time, The problem of induction can be phrased as follows: How can we ever reach a general conclusion about a state of affairs or a set of events if we have no guarantee as to its validity. In other words: is induction rational? however, we have reached a conclusion about an infinite set of events from a finite number of observations of the event. 3 1 Excluding parentheses and footnotes. 2 Example partly taken from Arnold Zuboff 3 Example due to David Hume Who can really tell for sure that the sun will go up tomorrow morning? As Bertrand Russell states, a chicken, having been fed by the farmer every morning of its life, wakes up in full expectation of being fed but to its great surprise finds that it is led directly to the

-3- slaughterhouse to have its head chopped off. 4 We might just as much wake up one morning, finding that the sun has not risen or that all objects start floating around in defiance of Earth's -4- "even after we have experience of the operations of cause and effect, our conclusions from that experience are not founded on reasoning, or any process of the understanding." 7 gravity. These are as much logically possible as the fact that the world might have come into existence five minutes ago, complete with our beliefs that it has existed for x million years. 5 The same problem of necessity can be applied to all other cases of induction 8 : do we have epistemic access to the necessity of X occuring when Y occurs? Hume thinks not, and In the remainder of this essay I want to expound on the problem of induction and clarify where the problems really lie. In part 2 I shall take a look at a general discussion of the problem of induction. In part 3 I shall look at how the problem relates to scientific method, through partly introspective reasons he finds a strong argument for his case, and hence induction for him is very problematic. I will leave this issue at the side for the moment and try to find an answer for Hume in part 4. taking a close look at how Karl Popper tried to solve the problem and arguing that Popper circumvented the problem without solving it. In part 4 I will discuss the problem of induction as it relates to epistemology and I will argue that the original problem is not so much a problem in itself, but that it leads to what I shall call 'the second problem of induction', which I will discuss in part 5. Besides its metaphysical problem, induction also comes across some problems related to the field of logic. There seems to be a burning urge to be able to defend induction with principles of deduction, in order to guarantee the validity of inductive conclusions. It quickly gets clear that inductive arguments cannot be defended by some deductive argument and therefore induction is not proof-theoretically logical. 2. The problem of induction: general discussion One line of denfence against this assertion is to say that inductive inferences are not A close analysis of the problem of induction is best started with the metaphysical problems it involves as to the problem of necessity. This problem can best be described with the example of cause and effect as discussed by David Hume. Hume asked the following question: when an event A causes an event B, what is it that necessitates event B occuring as 100% valid nor are they 100% invalid, but that they are probable to a degree between 0 and 100%. This argument does not take us very far however, since the probability expressed is still global, whereas the evidence to back up this probability is still taken from a finite number of observations. The probability argument therefore cannot escape the problem of induction. a result of event A occuring. Furthermore, if we accept this necessity, is there any way in which we can access this necessity conciously, i.e. through reflection. 6 Hume asserts that Another line of defence is that induction can be defended by induction: we have seen that induction has been succesful in the past and that therefore it will be successful in the 4 The Problems of Philosophy, 1912:35 5 and this is just as logically possible as the fact that we may the figment of the mind of some evil demon: the notion of skepticism comes in here very strongly and I shall return to that issue later on. 6 As Hume puts it: "When it is asked What is the nature of all our reasonings and conclusions concerning [the] relation [of cause and effect]? it may be replied in one word, Experience. But if we... ask What is the foundation of all conclusions from experience? this implies a new question, which may be of more difficult solution and explication". (Hume 1955:32) future. Deductivists hold that this argument presents a vicious circularity. However, as David Papineau 9 quite rightly points out, even deduction falls victim to this sort of circularity: the 7 David Hume An Essay Concerning Human Understanding, Chapter 4.2. 8 I take it here that the assumed causal relation between two types of event always occuring together is an example of induction. 9 David Papineau, Philosophical Naturalism, 1993:158

-5- -6- logical rules that are used to prove the overall validity of deduction are themselves derived through deduction. 10 But has it? Popper seems to ignore the fact that even a falsifying observation is very much subject to the problem of induction. Obviously a falsifying observation will not be I now want to turn to the philosophy of science, and see the attempt made by Karl Popper to solve the problem of induction with this specific field in mind. relied upon when it is just made once, so the observation is emulated over and over again, in order to ensure that the falsification really is a falsification and not just merely some experimental error. But is not this repetition of falsifying observations just induction? 3. Induction and Science In addition to this problem, Popper has been said to give not only a dubious account of The philosophy of science is very much concerned with the problem of induction. The issues here are of two types: normative and descriptive. In other words, to what extent does induction actually play a part in scientific method and to what extent should it. The naïve inductivist can be said to claim that "If a large number of As have been observed under a wide how science should be handled, but also of how it has been handled. Thus, falsificationism is a bad description of a history of science that has brought us a great many scientific discoveries, and to reduce all future science to falsificationism would be to exclude all the valuable methods of the past. 11 variety of conditions, and if all those observed As without exception possessed the property B, then all As have property B." (Chalmers 1978:5). This position has its obvious drawbacks: 4. Induction and Epistemology: is there really a problem? how large is large? How wide is wide? And then there is the obvious problem of induction as stated above: where is the guarantee? In epistemology it is undisputed (and indeed undisputable) that beliefs are formed through using inductive inferences and not merely deductive ones. The problem of induction, Karl Raimund Popper claimed that inductivism is and should not be a tool of scientific enterprise. He offered an alternative that he thought would sweep the problem of induction out of the way: falsificationism. In short, Popper claimed that science was an ongoing process as seen from an epistemological point of view, can thus be formulated as: How can we really know about something if our knowledge is based on beliefs which are inferred inductively. of conjectures and refutation of conjectures through falsification, and that any conjecture that was not capable of being falsified was not worthy of being scientific and was thus pseudoscientific. Inductive methods play no part and hence the problem of induction can virtually be induction? At this point I would like to raise the question: is there really a problem with ignored and therefore has been "solved" as far as it concerncs science. 10 Papineau says that both the deductive defence of deduction and the inductive defence of induction are circular, but they are not premise-circular (ie the conclusion is not contained among the premises) which would make them vicious, but they are rule-circular, which does not necessarily make the argument vicious. Goodman even says that such circularity can be seen to be virtuous. (Papineaus 1993:157 ; Goodman 1953:64) 11 Recent theories by the likes of Imre Lakatos, Thomas Kuhn and Paul Feyerabend try to incorporate both the historical and the normative aspects of a method of science by describing science as a more holistic research program, where observation and theory interactively support and refute each other. (Chalmers 19

-7- Above I have presented the argument that induction is not logical and hence not rational. I very much think that we are committing a semantic fallacy if we equate rational -8- that is needed to recognise the necessity of the recurrence of events that Hume was looking for. with logical. 12 If we do equate the two, then we can agree with the critics of induction: nobody ever claimed that induction was logically correct. The above argument may seem a bit unphilosophical in its nature, but if we allow our sensory organs to be sources of knowledge - and our sensory organs developed in an How about the claim that we lack the access to a notion of necessity needed to justify evolutionary way that made them functional for our survival and for knowledge - then why shouldn't we be able to ascribe the same importance to induction. our inductive reasoning? At this point I would like to propose what I call a genealogicalfunctional view of induction, that will do away with many of the problems. Let us imagine the following scenario: we are in a state of nature, where all around us there are animals that reason in all sorts of ways. Some reason inductively, others reason completely randomly, others (Descartes would be especially fond of these) reason purely deductively, and others reason in a counter-inductive way 13. What happens in such a world? Animals begin to die because their method of reasoning is not functionally adapted to the environment. The counter-inductivists and the deductivists probably go first (the latter dying of starvation while trying to deduce if the fruit before them really exists), followed by those that reason To conclude this section I want to answer the question: is there really a problem with induction? I would argue that there isn't, if one takes a looser reading of the word. If the problem is that we can't argue logically for induction, then this is surely a problem, but is it necessarily so big as to be called the problem? Arguably not, and I think that if we relied entirely on deduction for knowledge and survival, we would be talking about a far bigger problem, namely the problem of deduction. Induction at least allows us to gain knowledge about the world, the same would not apply if we relied merely on deduction. randomly. Who's left: the inductivists. My point here is that as human beings we have, through evolution, functionally adapted to use induction via a mechanism designated as conditioning. It can be argued that this conditioning-mechanism is precisely the mechanism 12 The following example shows the semantic problems we encounter when trying to apply the concept 'rational' to the way we think. Imagine the following scenario: we are in the postoffice, the queue is enormous, mostly due to the fact that only one counter out of 20 is open. The man in front of us is getting really impatient, and once he is at the counter he starts screaming at the man behind the counter in a very abusive manner, because he had to wait so long in the queue. The rest of us in the queue might have observed that the man behind the counter was doing his utmost to work quickly and may murmur something to the extent that the screaming customer is behaving irrationally. When we say that, however, we are not in any way referring to his lack of deductive reasoning that we are all employing. We probably decided not to yell at the man behind the counter for a reason that was derived in an equally inductive manner. We still considered ourselves rational, however, and our designation of the angry customer as being irrational was based far more on the way he reasoned inductively, not the mere fact that he was reasoning inductively. 13 i.e. they generalise that things will not happen the way they have always happened so far. Lemmings may be a species of animals who miserably fail to apply the principle of induction when year after year, they go and jump in the sea, not learning a lesson from their ancestors, who all failed to return when they were also 'just going for a quick swim'. But I think there is a second problem related to induction, which is: when is induction a reliable source of knowledge. It is to this question I want to turn now. 5. The use of induction The second problem of induction can be formulated as follows: Under what circumstances do inductively inferred beliefs constitute knowledge? In other words: how should induction be used and how should it not be used, if it shold contribute to knowledge? As in opposition to science, we cannot afford the luxury of leaving the question open, since the discipline of epistemology requires definite answers. One way of answering the above question is to say that induction should be reliable. But this does not bring us much

-9- further, since we still have to define reliable, and attempts to do this often end up with an inductive defence of induction 14. -10- a potential opponent: a theory has then advanced to such an extent that only the most radical counterexamples could bring it down. And there is no doubt that the burden of proof in this case lies with the skeptics. Another way to define the right circumstances for the use of induction has been by using the notion of coherentism. 15 Coherentists would argue that an inductive inference would be justified if it is coherent with the rest of our beliefs. Coherentism takes us a long way, but there are some problems with it, as there are with coherentism in general 16. As we can see, the task of defining the right usage of induction is not an easy one in epistemology. I have tried to briefly present a few solutions that are mutually compatible, but Bibliography Audi, R. (1998) Epistemology. London: Routledge Chalmers, A.F. What is this Thing called Science? Dancy, J. (1985) Introduction to Contemporary Epistemology, Oxford: Basil Blackwell Grayling, A.C. (1995) Philosophy, a guide through the Subject, Oxford: OUP Hume, D. (1955) An Enquiry Concerning Human Understanding, ch.4.2. Papineau, D. (1993) Philosophical Naturalism, Oxford Popper, K.R. (1959) The Logic of Scientific Discovery, London: Hutchinson need to point out, however, that the debate is still very much in action and that no solution has been generally agreed upon. 6. Conclusion At the beginning of this essay, I asked the question if the problem of induction could be solved? In this essay I have tried to show that we have to be careful about what the problem of induction really is and have concluded that there are really two problems. I have argued that the original problem of induction indeed cannot be solved, but that - at the same time - it is not really that much of a problem. Instead, it leads us to a second problem of induction, which is to find the circumstances in which induction can be seen as justifiable. And this seemed to pose us with a much bigger problem. To conclude, I want to add that my discussion of the subject of induction has very much let skepticism back in as a serious problem: the sun may indeed not rise tomorrow. But, as is often the case in epistemology, there is something comforting about having skepticism as 14 Papineau in Grayling 1995:136 15 Dancy 1985:208 16 eg are our sets of beliefs really coherent?